Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 13 LLMs and 10 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5× speedup while retaining > 96\% of reasoning performance without extra modules or hyperparameter tuning. This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.
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Computer Vision · 3D Rendering & Reconstruction
We propose a 3D latent representation that jointly models object geometry and view-dependent appearance. Most prior works focus on either reconstructing 3D geometry or predicting view-independent diffuse appearance, and thus struggle to capture realistic view-dependent effects. Our approach leverages that RGB-depth images provide samples of a surface light field. By encoding random subsamples of this surface light field into a compact set of latent vectors, our model learns to represent both geometry and appearance within a unified 3D latent space. This representation reproduces view-dependent effects such as specular highlights and Fresnel reflections under complex lighting. We further train a latent flow matching model on this representation to learn its distribution conditioned on a single input image, enabling the generation of 3D objects with appearances consistent with the lighting and materials in the input. Experiments show that our approach achieves higher visual quality and better input fidelity than existing methods.
Reinforcement Learning · Deep RL
Reinforcement Learning (RL) in partially observable environments poses significant challenges due to the complexity of learning under uncertainty. While additional information, such as that available in simulations, can enhance training, effectively leveraging it remains an open problem. To address this, we introduce Guided Policy Optimization (GPO), a framework that co-trains a guider and a learner. The guider takes advantage of privileged information while ensuring alignment with the learner's policy that is primarily trained via imitation learning. We theoretically demonstrate that this learning scheme achieves optimality comparable to direct RL, thereby overcoming key limitations inherent in existing approaches. Empirical evaluations show strong performance of GPO across various tasks, including continuous control with partial observability and noise, and memory-based challenges, significantly outperforming existing methods.
Reinforcement Learning · Deep RL
Flow-matching policies hold great promise for reinforcement learning (RL) by capturing complex, multi-modal action distributions. However, their practical application is often hindered by prohibitive inference latency and ineffective online exploration. Although recent works have employed one-step distillation for fast inference, the structure of the initial noise distribution remains an overlooked factor that presents significant untapped potential. This overlooked factor, along with the challenge of controlling policy stochasticity, constitutes two critical areas for advancing distilled flow-matching policies. To overcome these limitations, we propose GoldenStart (GS-flow), a policy distillation method with Q-guided priors and explicit entropy control. Instead of initializing generation from uninformed noise, we introduce a Q-guided prior modeled by a conditional VAE. This state-conditioned prior repositions the starting points of the one-step generation process into high-Q regions, effectively providing a ``golden start'' that shortcuts the policy to promising actions. Furthermore, for effective online exploration, we enable our distilled actor to output a stochastic distribution instead of a deterministic point. This is governed by entropy regularization, allowing the policy to shift from pure exploitation to principled exploration. Our integrated framework demonstrates that by designing the generative startpoint and explicitly controlling policy entropy, it is possible to achieve efficient and exploratory policies, bridging the generative models and the practical actor-critic methods. We conduct extensive experiments on offline and online continuous control benchmarks, where our method significantly outperforms prior state-of-the-art approaches.
Theory · Learning Theory
Two pressing topics in the theory of deep learning are the interpretation of feature learning (FL) mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich FL often appear in the form of high-dimensional non-linear equations, which require computationally intensive numerical solutions. Given the many details that go into defining a deep learning problem, this analytical complexity is a significant and often unavoidable challenge. Here, we propose a powerful heuristic route for predicting the data and width scales at which various patterns of FL emerge. This form of scale analysis is considerably simpler than such exact theories and reproduces the scaling exponents of various known results. In addition, we make novel predictions on complex toy architectures, such as three-layer non-linear networks and attention heads, thus extending the scope of first-principle theories of deep learning.
Reinforcement Learning · Deep RL
Reinforcement Learning with verifiable rewards (RLVR) has emerged as a primary learning paradigm for enhancing the reasoning capabilities of multi-modal large language models (MLLMs). However, during RL training, the enormous state space of MLLM and sparse rewards often leads to entropy collapse, policy degradation, or over-exploitation of suboptimal behaviors. This necessitates an exploration strategy that maintains productive stochasticity while avoiding the drawbacks of uncontrolled random sampling, yielding inefficient exploration. In this paper, we propose CalibRL, a hybrid-policy RLVR framework that supports controllable exploration with expert guidance, enabled by two key mechanisms. First, a distribution-aware advantage weighting scales updates by group rareness to calibrate the distribution, therefore preserving exploration. Meanwhile, the asymmetric activation function (LeakyReLU) leverages the expert knowledge as a calibration baseline to moderate overconfident updates while preserving their corrective direction. CalibRL increases policy entropy in a guided manner and clarifies the target distribution by estimating the on-policy distribution through online sampling. Updates are driven by these informative behaviors, avoiding convergence to erroneous patterns. Importantly, these designs help alleviate the distributional mismatch between the model’s policy and expert trajectories, thereby achieving a more stable balance between exploration and exploitation. Extensive experiments across eight benchmarks, including both in-domain and out-of-domain settings, demonstrate consistent improvements, validating the effectiveness of our controllable hybrid-policy RLVR training. Code is available at https://github.com/zhh6425/CalibRL.
Reinforcement Learning · Deep RL
Reinforcement Learning with Verifiable Reward (RLVR) has equipped large language models (LLMs) with the capability of reasoning over complicated logical problems through policy optimization. However, conventional methods require complete annotation of the entire dataset and allocate computation uniformly over all samples. We articulate the lottery sample hypothesis in policy optimization of LLMs: a large training set contains a small subset that, when trained alone, yields performance comparable to that of the full dataset. This paper therefore explores the following question: How can we identify these lottery-winning samples from the original dataset without access to answers? Unlike prior efforts that analyze the effect of different samples in the training set with complete annotation, this paper focuses on the unsupervised discovery of critical instances for LLM reasoning and proposes a novel framework termed Complementary Conformal Selection (CONST). Specifically, CONST evaluates the importance of samples by considering two complementary components: procedural volatility and outcome volatility. Procedural volatility measures the potential variations during the LLM’s reasoning process, while outcome volatility captures inconsistencies in the final answer. Subsequently, conformal prediction is used to obtain a prediction set whose cardinality serves as the criterion for selecting the lottery-winning samples for annotation. We also provide a theoretical analysis, showing that CONST can effectively approximate the optimal policy. Extensive experiments on various LLMs across different datasets demonstrate the effectiveness of CONST.
Reinforcement Learning · Deep RL
Reinforcement learning with verifiable rewards has significantly advanced reasoning with large language models (LLMs) in domains such as mathematics and logic. However, verifiable signals provide only coarse-grained or binary correctness feedback. This limitation results in inefficiencies like overly verbose or repetitive reasoning. Existing length-based solutions (e.g., length penalty) compromise accuracy. To address this deficiency, we introduce **self-aligned reward (SAR)**, a generic, universally applicable self-guided signal that complements verifiable rewards to enhance both reasoning accuracy and efficiency in RL. Specifically, SAR is defined as the relative perplexity difference between an answer conditioned on the query and the standalone answer, thereby favoring responses that are concise and query-specific. Quantitative analysis reveals that SAR reliably judges answer quality: concise, correct answers score higher than redundant ones, and partially correct answers score higher than entirely incorrect ones. Evaluation on 4 different models across 7 benchmarks shows that integrating SAR with prevalent RL algorithms like PPO and GRPO reduces answer length by 30%, while improving accuracy by 4%. Our analysis also shows that SAR generalizes well to out-of-domain tasks and achieves a Pareto-optimal frontier between correctness and efficiency compared to state-of-the-art baselines. We also show that SAR shortens unnecessary elaboration while preserving advanced reasoning behaviors. These results highlight the promise of self-aligned reward as a fine-grained complement to verifiable rewards, paving the way for efficient and effective LLM training. All of our code implementations and data are publicly available at GitHub.
Reinforcement Learning · Deep RL
Large language models (LLMs) are increasingly expected to tackle complex tasks, driven by their expanding applications and users' growing proficiency in crafting sophisticated prompts. However, as the number of explicitly stated requirements increases (particularly more than $10$ constraints), LLMs often struggle to accurately follow such complex instructions, which limits their applicability in complex real-world scenarios. To the best of our knowledge, existing datasets do not exceed 10 constraints per instance. To address this challenge, we propose RECAST, an efficient and scalable framework for synthesizing datasets where each example incorporates far more constraints than those in existing benchmarks, aiming to challenge and extend the boundaries of models’ ability to follow complex instructions. These constraints are extracted from real-world prompt-response pairs to ensure practical relevance. Using this framework, we construct RECAST-$30$K, a large-scale, high-quality dataset comprising $30$k instances spanning $19$ constraint types. Experimental results demonstrate that models fine-tuned on RECAST-30K substantially improve in following complex instructions while maintaining their general capabilities without degradation. Moreover, RECAST enables automatic verification of constraint satisfaction via rule-based validators for quantitative constraints and LLM-based validators for qualitative ones, the verifiability provided by RECAST enables the design of reward functions for reinforcement learning, which further boosts model performance on complex and challenging tasks.
Reinforcement Learning · Deep RL
Balancing exploration and exploitation remains a central challenge in reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs). Current RLVR methods often overemphasize exploitation, leading to entropy collapse, diminished exploratory capacity, and ultimately limited performance gains. Although techniques that increase policy stochasticity can promote exploration, they frequently fail to escape dominant behavioral modes. This creates a self-reinforcing loop—repeatedly sampling and rewarding dominant modes—that further erodes exploration. We introduce **E**xploration-**E**nhanced **P**olicy **O**ptimization (**EEPO**), a framework that promotes exploration via two-stage rollouts with adaptive unlearning. In the first stage, the model generates half of the trajectories; it then undergoes a lightweight unlearning step to temporarily suppress these sampled responses, forcing the second stage to explore different regions of the output space. This *sample-then-forget* mechanism disrupts the self-reinforcing loop and promotes wider exploration during rollouts. Across five reasoning benchmarks, EEPO outperforms GRPO, achieving average relative gains of 24.3\% on Qwen2.5-3B, 33.0\% on Llama3.2-3B-Instruct, and 10.4\% on Qwen3-8B-Base.
Studies have shown that catastrophic forgetting primarily stems from the difficulty of reactivating old memories; although parameter-efficient fine-tuning can mitigate forgetting while keeping most model parameters frozen, it still falls short in fully reawakening knowledge of prior tasks. In contrast, humans can efficiently retrieve and flexibly integrate existing experiences when learning new tasks, thereby maintaining stable performance on earlier ones. During cognition, the hippocampal EC–DG–CA3–CA1 circuit engages in multiple rounds of associative recall, and its pattern-separation and memory-completion mechanisms excel at activating historical information. Inspired by this mechanism, we propose HippoTune, a latent-space iterative retrieval strategy that embeds a query–retrieve–feedback loop within each Transformer layer. Starting from the hidden state as an initial query, the model performs a few rounds of soft key–value retrieval, projects the retrieved signals back into the query, and updates it iteratively until convergence or a preset iteration limit. Theoretically, we show this process implements a Krylov-style polynomial approximation, equivalent to a differentiable second-order preconditioner, thereby deepening retrieval in a principled way. Empirically, HippoTune outperforms classical buffer-free PEFT-CL methods by 5–8\% in accuracy across three vision benchmarks, while reducing training FLOPs by 50\%, effectively mitigating forgetting under tight compute constraints. Code is available at: https://github.com/yan4xi1/HippoTune.
Reinforcement Learning · Deep RL
Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for complex reasoning tasks with clear correctness signals such as math and coding. However, extending it to real-world reasoning tasks is challenging, as evaluation depends on nuanced, multi-criteria judgments rather than binary correctness. Instance-specific rubrics have recently been used in evaluation benchmarks to capture such judgments, but their potential as reward signals for on-policy post-training remains underexplored. We introduce $\textbf{Rubrics as Rewards (\textit{RaR})}$, an on-policy reinforcement learning method that extends RLVR beyond verifiable domains by using rubric-based feedback. Across both medical and science domains, we evaluate multiple strategies for aggregating rubric feedback into rewards. The best RaR variant achieves relative improvements of up to 31\% on HealthBench and 7\% on GPQA-Diamond over popular LLM-as-judge baselines that rely on direct Likert-based rewards. These results demonstrate that RaR-trained policies adapt well to diverse evaluation formats, performing strongly on both rubric-based and multiple-choice tasks. Moreover, we find that using rubrics as structured reward signals yields better alignment for smaller judges and reduces performance variance across judge scales.
Reinforcement Learning · Deep RL
Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.
Reinforcement Learning · Deep RL
Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models. Howerer, existing methods rely solely on outcome rewards, without explicitly optimizing verification or leveraging reliable signals from realistic environments, leading to unreliable self-verification and limited test-time scaling. To address this, we widen the verification–generation asymmetry by explicitly optimizing self-verification, making it a reliable driver of deeper test-time scaling. We introduce ReVeal, a multi-turn Reinforcement learning framework that evolves code generation through self-Verification and tool-based evaluation. ReVeal structures long-horizon reasoning as iterative generation–verification turns and incorporates TAPO for turn-level credit assignment, fostering the co-evolution of code and test generation. At inference, this strengthened self-verification enables the model to use self-constructed tests and tool feedback to continuously evolve code for 20+ turns on LiveCodeBench despite training on only three. It also significantly improves Pass@k, indicating stronger exploration that expands the reasoning boundaries of the base model. These findings highlight the promise of ReVeal as a scalable paradigm for RL training and test-time scaling, paving the way for more robust and autonomous AI agents. Code is available at [https://ReVeal.github.io/](https://shimly-2.github.io/ReVeal.github.io/).
Optimization · Large Scale, Parallel and Distributed
In this paper, we study coreset construction for LASSO regression, where a coreset is a small, weighted subset of the data that approximates the original problem with provable guarantees. For unregularized regression problems, sensitivity sampling is a successful and widely applied technique for constructing coresets. However, extending these methods to LASSO typically requires coreset size to scale with O(\mathcal{G}d), where d is the VC dimension and \mathcal{G} is the total sensitivity, following existing generalization bounds. A key challenge in improving upon this general bound lies in the difficulty of capturing the sparse and localized structure of the function space induced by the \ell_1 penalty in LASSO objective. To address this, we first provide an empirical process-based method of sensitivity sampling for LASSO, localizing the procedure by decomposing the functional space into separate components, which leads to tighter estimation error. By carefully leveraging the geometric properties of these localized spaces, we establish tight empirical process bounds on the required coreset size. These techniques enable us to achieve a coreset of size \tilde{O}(\epsilon^{-2}d\cdot(\log^3 d\cdot\min\{1,\log d/\lambda^2\}+\log(1/\delta))), which ensures a (1\pm\epsilon)-approximation for any \epsilon,\delta\in(0,1) and \lambda > 0. Furthermore, we give a lower bound showing that any algorithm achieving a (1+\epsilon)-approximation must select at least $Omega(\frac{d\log{d}}{\epsilon^2}) rows in the regime where \lambda=O(d^{-1/2}). Empirical experiments show that our proposed algorithm is at least 4 times faster than the existing LASSO solver and more than 9 times faster on half of the datasets, while ensuring high solution quality and sparsity.
Reinforcement Learning · Deep RL
Representation learning is critical to the empirical and theoretical success of reinforcement learning. However, many existing methods are induced from model-learning aspects, misaligning them with the RL task in hand. This work introduces the Spectral Bellman Method, a novel framework derived from the Inherent Bellman Error (IBE) condition. It aligns representation learning with the fundamental structure of Bellman updates across a space of possible value functions, making it directly suited for value-based RL. Our key insight is a fundamental spectral relationship: under the zero-IBE condition, the transformation of a distribution of value functions by the Bellman operator is intrinsically linked to the feature covariance structure. This connection yields a new, theoretically-grounded objective for learning state-action features that capture this Bellman-aligned covariance, requiring only a simple modification to existing algorithms. We demonstrate that our learned representations enable structured exploration by aligning feature covariance with Bellman dynamics, improving performance in hard-exploration and long-horizon tasks. Our framework naturally extends to multi-step Bellman operators, offering a principled path toward learning more powerful and structurally sound representations for value-based RL.
Reinforcement Learning · Deep RL
Reinforcement Learning (RL) has emerged as a popular training paradigm, particularly when paired with reasoning models. While effective, it primarily focuses on generating responses and lacks mechanisms to explicitly foster critique or reflection. Several recent studies, like Critique-Fine-Tuning (CFT) and Critique-Guided-Distillation (CGD) have shown the benefits of explicitly teaching LLMs how to critique. Motivated by them, we propose Critique Reinforcement Learning (CRL), where the model is tasked with generating a critique for a given (question, solution) pair. The reward is determined solely by whether the final judgment label $c \in \{\texttt{True}, \texttt{False}\}$ of the generated critique aligns with the ground-truth judgment $c^*$. Building on this point, we introduce Critique-Coder, which is trained on a hybrid of RL and CRL by substituting 20\% of the standard RL data with CRL data. We fine-tune multiple models (Critique-Coder) and evaluate them on different benchmarks to show their advantages over RL-only models. We show that Critique-Coder consistently outperforms RL-only baselines on all the evaluated benchmarks. Notably, our Critique-Coder-8B can reach over 60\% on LiveCodeBench (v5), outperforming other reasoning models like DeepCoder-14B and GPT-o1. Beyond code generation, Critique-Coder also demonstrates enhanced general reasoning abilities, as evidenced by its better performance on logic reasoning tasks from the BBEH dataset. This indicates that the application of CRL on coding datasets enhances general reasoning and critique abilities, which are transferable across a broad range of tasks. Hence, we believe that CRL works as a great complement to standard RL for LLM reasoning.
Applications · Neuroscience, Cognitive Science
Generalization in EEG-based motor imagery (MI) brain-computer interfaces (BCIs) is hampered by cross-subject and cross-session variability. Although large-scale EEG pretraining has advanced representation learning, their practical deployment is hindered by the need for costly fine-tuning to overcome significant domain shifts. Test-time adaptation (TTA) methods that adapt models during inference offer a promising solution. However, existing EEG-TTA methods either rely on gradient-based fine-tuning (suffering from high computational cost and catastrophic forgetting) or data alignment strategies (failing to capture shifts in temporal predictive embeddings). To address these limitations, we propose BTTA-DG, a novel Bayesian Test-Time Adaptation framework that performs efficient, gradient-free adaptation by modeling the distribution of temporal predictive embeddings. Our approach first employs a lightweight SincAdaptNet with learnable filters to extract task-specific frequency bands. We then introduce a novel Dirichlet feature projection that maps temporal embeddings onto a compact and interpretable parameter space, effectively capturing the concentration of time-varying predictive evidence. Adaptation is achieved via a GMM-driven Bayesian inference mechanism, which models the historical distribution of these Dirichlet parameters and fuses this evidence with the model's prior predictions to calibrate outputs for the target domain. Extensive experiments show that BTTA‑DG significantly outperforms previous EEG‑TTA methods, achieving state‑of‑the‑art accuracy while running at real‑time speed. Furthermore, visualizations confirm the physiological interpretability of our learned filters and the robust class separability of our Dirichlet feature space.
Computer Vision · Classification and Understanding
Fine-Grained Visual Classification (FGVC) aims to distinguish visually similar subcategories within a broad category, and poses significant challenges due to subtle inter-class differences, large intra-class variations, and data scarcity. Existing methods often struggle to effectively capture both part-level detail and spatial relational features, particularly across rigid and non-rigid object categories. To address these issues, we propose Part-level Semantic-guided Contrastive Learning (PSCL), a novel framework that integrates three key components. (1) The Part Localization Module (PLM) leverages clearCLIP to enable text-controllable region selection, achieving decoupled and semantically guided spatial feature extraction. (2) The Multi-scale Multi-part Branch Progressive Reasoning (MMBPR) module captures discriminative features across multiple parts and scales, while reducing inter-branch redundancy. (3) The Visual-Language Contrastive Learning based on Multi-grained Text Features (VLCL-MG) module introduces intermediate-granularity category concepts to improve feature alignment and inter-class separability. Extensive experiments on five publicly available FGVC datasets demonstrate the superior performance and generalization ability of PSCL, validating the effectiveness of its modular design and the synergy between vision and language. Code is available at: https://github.com/joker-lin9/PSCL
Reinforcement Learning · Batch/Offline
Offline reinforcement learning enables policy learning solely from fixed datasets, without costly or risky environment interactions, making it highly valuable for real-world applications. While Transformer-based approaches have recently demonstrated strong sequence modeling capabilities, they typically learn from complete trajectories conditioned on final returns. To mitigate this limitation, we propose the Peak-Return Greedy Slicing (PRGS) framework, which explicitly partitions trajectories at the timestep level and emphasizes high-quality subtrajectories. PRGS first leverages an MMD-based return estimator to characterize the distribution of future returns for state-action pairs, yielding optimistic return estimates. It then performs greedy slicing to extract high-quality subtrajectories for training. During evaluation, an adaptive history truncation mechanism is introduced to align the inference process with the training procedure. Extensive experiments across multiple benchmark datasets indicate that PRGS significantly improves the performance of Transformer-based offline reinforcement learning methods by effectively enhancing their ability to exploit and recombine valuable subtrajectories.